"to cut off," originally of branches of a tree, mid-15c. (implied in lopped; place name Loppedthorn is attested from 1287), a verb from Middle English loppe (n.) "small branches and twigs trimmed from trees" (early 15c.), which, along with Medieval Latin loppa, is of unknown origin. Related: Lopping.

"droop, hang loosely," as do the ears of certain dogs and rabbits, 1570s, probably a variant of lob or of lap (v.); compare lopsided (1711), which in early use also was lapsided. Lop-eared attested from 1680s. Related: Lopped; lopping.